Which flowers should NOT be offered to certain gods?
the best-known customs are no ketakī to Śiva, no tulasī to Gaṇeśa, and no wilted, fallen or smelled flowers to anyone.
A few prohibitions are widely followed, each with a Purāṇic story behind it. Ketakī (screw-pine) is not offered to Śiva — tradition says it falsely testified for Brahmā about finding the top of Śiva’s infinite pillar of light. Tulasī is generally not offered to Gaṇeśa, following a story of a quarrel between them, though some families offer it on Gaṇeśa Caturthī. Many also avoid offering tulasī to Śiva, and some avoid dūrvā for Devī.
General rules apply to all deities: do not offer flowers that are wilted, insect-eaten, picked from the ground (except naturally fallen pārijāta in many traditions), already smelled, or taken without permission from someone else’s garden. Flowers without fragrance or with strong unpleasant smells are often avoided.
Customs differ by region and sampradāya, so if your family has its own list, follow it. Do not worry about mistakes made unknowingly; sincerity is always accepted.
Ketakī not for Śiva; tulasī not for Gaṇeśa · Source: Purāṇic stories; family custom
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